1.
Innovative Systems Design and Engineering
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.4, No.14, 2013
www.iiste.org
Analysis of Wind Turbine Driven Permanent Magnet
Synchronous Generator under Different Loading Conditions
Gaber El Saady* , El-Nobi A.Ibrahim, Hamdy Ziedan and Mohammed M.Soliman
Electric Engineering Department, Assiut University, Assiut, Egypt
* E-mail of the corresponding author: gaber1@yahoo.com
Abstract
This paper proposes the configuration of a Wind Turbine generating system equipped with Permanent Magnet
Synchronous Generator (PMSG). There are different types of synchronous generators, but the PMSG is chosen
which has better performance due to higher efficiency and less maintenance. Since it can be used without a gearbox
also implies a reduction of the weight of the nacelle and a reduction of costs. The model includes a wind turbine
model, drive train model and PMSG model. The equations that explain their behavior have been introduced. The
generator model is established in the d-q synchronous rotating reference frame. The proposed Wind Turbine
Generator System (WTGS) has been implemented in MATLAB/SIMULINK software. The PMSG is operating in
stand-alone which is loaded with different types of loads. The simulation results indicate the ability of wind driven
PMSG to operate over wide range of operating conditions at different loading conditions and show effect of different
load types in operation.
Keywords: Permanent Magnet Synchronous Generator (PMSG), Wind Turbine, Wind Energy and WTGS
MATLAB/SIMULINK.
1. Introduction
During the last few decades, wind energy became the most competitive form of clean, non-polluting and renewable
energy to provide a sustainable supply to the world development (Chen et al. 2012) which worldwide wind capacity
doubled approximately every three years. Currently, five countries (Germany, USA, Denmark, India and Spain)
concentrate more than 83% of worldwide wind energy capacity in their countries. The need for increased power
production from the wind and economic reasons, when the rated power of today’s wind turbines is still relatively
small (2MW units are now typical), makes it necessary to group wind turbines into so-called wind farms( Rolan' et al.
2009).Wind farms are built on land, but in recent years there has been(and will be in the future) a strong trend
towards locating them offshore this due to the lack of suitable wind turbine sites on land and the highest wind
speeds located near the sea(and consequently higher energy can be extracted from the wind).
Both induction and synchronous generators can be used for wind turbine systems (Slootweg et al. 2003). Mainly,
three types of induction generators are used in wind power conversion systems: cage rotor, wound rotor with slip
control and doubly fed induction rotors .The last one is the most utilized in wind speed generation because it
provides a wide range of speed variation. However, the variable speed directly driven multi-pole permanent magnet
synchronous generator (PMSG) wind architecture is chosen for this purpose and it is going to be modelled: it offers
better performance due to higher efficiency, simple structure, reliable operation, low noise and less maintenance
because it does not have rotor current. What is more, PMSG can be used without a gearbox, which implies a
reduction of the weight of the nacelle and reduction of costs and so on ( Rolan' et al. 2009).This investigation
presents the model of a PMSG WT able to work under low and fast wind speed conditions and during wind gusts
( López-Ortiz et al. 2012).
The general goal of this paper is to model the electromechanical energy conversion system of Standalone wind
turbine driven with PMSG. Optimum wind energy extraction is achieved by running the Wind Turbine Generator
(WTG) invariable speed because of the higher energy gain and the reduced stresses with using the (PMSG) the
design can be even more simplified.
Simulations have been implemented with the software MATLAB/ SIMULINK to validate the model.
2. System structure and analysis
A typical structure of wind energy conversion system with PMSG consists of a wind turbine, drive train and PMSG.
97

2.
Innovative Systems Design and Engineering
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.4, No.14, 2013
www.iiste.org
2.1. Wind Energy Conversation
The kinetic energy of the wind is given by the following equation (S.VIJAYALAKSHMI et al. 2011):
Ec =
1
(1)
2mv2
m = ρvA∆t
(2)
Where: m is the air mass, v is the wind speed, A is the covered surface of the turbine and 𝜌 is the air density.
The wind power Pw has the following expression:
𝑑
𝑃𝑤 =
𝐸𝑐 =
𝑑𝑡
1
𝜌𝐴𝑣 3
2
(3)
The power coefficient of the turbine Cp can be defined by following equation:
Cp =
Pm
;
Pw
CP < 1
(4)
So the extracted power is given by:
1
Pm = Cp ρπR2 v 3
2
(5)
2
Where: A is area swept by the rotor (A = πR ), R is radius of the turbine rotor and Pm is the mechanical power that
extracts from the wind.
The power coefficient Cp (betz coefficient) reaches maximum value =0.593. In practice, values of obtainable power
coefficient’s are in the range of 45 percent which depends of the tip speed ratio ʎ of the wind turbine and angle of the
blades ß.
Cp = Cp(ʎ, ß)
(6)
The amount of aerodynamic torque is obtained from the power:
𝑇𝑚 =
Substitute from ʎ =
Pm
w
=
1
Cp ρπR2
2
v3
(7)
𝑤
Rw
(8)
v
𝑇𝑚 =
Often the torque coefficient CT =
1
ρπR3 v 2
2
Cp
(9)
ʎ
CP
(10)
ʎ
1
Tm = CT ρπR3 v 2
So,
(11)
2
2.2 The power coefficient of the turbine
The power coefficient can be utilized in the form of look-up tables or in form of a function. The second approach is
presented below (Slootweg et al. 2003), where the power coefficient is defining as a function of the tip-speed ratio
ʎ and the blade pitch angle ß as
𝐶 𝑝 (ʎ, ß) = 0.5 (
116
𝑄
− 0.4ß − 5) 𝑒
21
𝑄
−
(12)
Where Q is represented as
Q=
1
1
0.035
−
ʎ+0.08ß 1+ß3
(13)
2.3 The variation of Cp
The simulation model is shown in Figure 1 which the variation of Cp with tip speed ratio ʎ at different values of
pitch angle ß, also the variation of Cp with pitch angle ß at different values of ʎ are obtained.
98

3.
Innovative Systems Design and Engineering
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.4, No.14, 2013
www.iiste.org
Figure 1. Power Coefficient cp
2.3.1 The variation of CP with the tip speed ratio ʎ for various values of the pitch angle β
The variation of CP with the tip speed ratio ʎ for various values of the pitch angle β is depicted in Figure 2. Thus, by
varying the pitch angle ß, the power coefficient can be changed and the power captured by the turbine can be
controlled.
power coefficent Cp & tip speed ratio curves
power coefficent Cp
0.5
ß
=0
ß
=5
ß
10
ß
=15
ß
=20
ß
=25
ß
=30
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
14
16
tip speed ratio(lambda)
Figure 2. Analytical Approximation of Cp (ʎ, ß) Curves
2.3.2
The variation of CP with pitch angle ß at different values of ʎ
The variation of CP with the pitch angle β for various values of the tip speed ratio ʎ is depicted in Figure 3. Thus, by
varying the tip speed ratio ʎ, the power coefficient can be changed and the power captured by the turbine can be
controlled.
99

5.
Innovative Systems Design and Engineering
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.4, No.14, 2013
www.iiste.org
Figure 4.
Drive Train Model
4. Generator Model
The PMSG is used to produce electricity from the mechanical energy obtained from the wind Turbine. In the PMSG,
the rotor magnetic flux is generated by permanent magnets which are placed on the rotor surface ( a non-salient-pole
PMSG)( Wu et al. 2011; Yin et al. 2007).
The main purpose of this case study is to modelling of PMSG from its equations. To simplify the analysis, The
PMSG is normally modeled in the rotor field (dq-axis) synchronous reference Frame, which the q-axis is 90o ahead
of the d-axis with respect to the direction of rotation. The rotor has two axes which the axis that is aligned with the
rotor and flux is called d-axis and the perpendicular axis to d-axis called q-axis ( Abedini 2008).
The flux caused by PM is in the direction of d-axis, the angle between stator axis and d-axis is called ϴe as shown in
Figure 5.
Figure 5. The Configuration of The Winding and PM in The PMSG
The synchronization between the d-q rotating reference frame and the abc-three phase frame is maintained by
utilizing a phase locked loop .To simplify the SG model of Figure 5, the following mathematical manipulations can
be performed.
The voltage equations for the synchronous generator are given by (16) and (17):
vds = −R s ids − wr ʎqs + pʎds
(16)
vqs = −R s iqs + wr ʎds + pʎqs
(17)
Where
ʎds = −Ld ids + ʎr
(18)
ʎqs = −Lq iqs
(19)
Where ʎr is the rotor flux which is constant in the PMSG so,
inductances .
Substitute from equations (18) and (19) in (16) and (17) yield
dʎr
dt
vds = −R s ids + wr Lq iqs − Ld pids
101
= 0 ; Ld and Lq are the stator dq-axis self-
(20)

7.
Innovative Systems Design and Engineering
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.4, No.14, 2013
5. 1
www.iiste.org
Loading of PMSG with Resistive Load
5.1.1 Loading PMSG with Fixed Resistive Load
The PMSG is loading with a three-phase resistive load R L= 5.5Ω, the block diagram and matlab simulation for the
model is shown in Figures. 7and 8 respectively.
Figure 7. Block Diagram for Simulation
Figure 8. Matlab Simulink Model
The dq-axis stator currents, ids and iqs in the synchronous frame rotating at the synchronous speed of wr are
calculated by the SG model. They are then transformed into the abc -axis stator currents ias, ibs, and ics in the
stationary frame through the dq/abc transformation. The calculated load voltages vas, vbs and vcs which are also
the stator voltages are transformed to the dq-axis voltages vds and vqs in the synchronous frame .These voltages
are then fed back to the SG model.
First , the PMSG is loaded with a three phase balanced resistive load Rl and operates at 320 rpm(.8 pu)at a given
wind speed ( the rotor speed is kept constant at 320 rpm due to assumption that the combined moments of inertia is
very large) .
The following Figure 9. Shows the currents and voltages at PMSG terminals.
ids,iqs,is (pu)
ids,iqs,is (pu)
0.5
0.4
iqs
0.3
is
ids
0.2
0.1
0
0
0.005
0.01
0.015
0.02
0.025
time(sec)
(a)
103
0.03
0.035
0.04
0.045
0.05

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